Term Rewriting System R:
[x, y]
f(x, a(b(y))) -> f(a(b(x)), y)
f(x, b(c(y))) -> f(b(c(x)), y)
f(x, c(a(y))) -> f(c(a(x)), y)
f(a(x), y) -> f(x, a(y))
f(b(x), y) -> f(x, b(y))
f(c(x), y) -> f(x, c(y))

Innermost Termination of R to be shown.

`   R`
`     ↳Dependency Pair Analysis`

R contains the following Dependency Pairs:

F(x, a(b(y))) -> F(a(b(x)), y)
F(x, b(c(y))) -> F(b(c(x)), y)
F(x, c(a(y))) -> F(c(a(x)), y)
F(a(x), y) -> F(x, a(y))
F(b(x), y) -> F(x, b(y))
F(c(x), y) -> F(x, c(y))

Furthermore, R contains one SCC.

`   R`
`     ↳DPs`
`       →DP Problem 1`
`         ↳Remaining Obligation(s)`

The following remains to be proven:
Dependency Pairs:

F(b(x), y) -> F(x, b(y))
F(a(x), y) -> F(x, a(y))
F(c(x), y) -> F(x, c(y))
F(x, c(a(y))) -> F(c(a(x)), y)
F(x, b(c(y))) -> F(b(c(x)), y)
F(x, a(b(y))) -> F(a(b(x)), y)

Rules:

f(x, a(b(y))) -> f(a(b(x)), y)
f(x, b(c(y))) -> f(b(c(x)), y)
f(x, c(a(y))) -> f(c(a(x)), y)
f(a(x), y) -> f(x, a(y))
f(b(x), y) -> f(x, b(y))
f(c(x), y) -> f(x, c(y))

Strategy:

innermost

Innermost Termination of R could not be shown.
Duration:
0:00 minutes